calculus
posted by Anonymous .
A rumor spreads through a population in such a way that "t" hours after the rumor starts, the percent of people involved in passing it on is given by P(t)=100[e^(t)e^(4t)]. What is the highest percent of people involved in spreading the rumor within the first 3 h? When does this occur?

Differentiate P(t) to obtain the derivative P'(t).
P'(t) = 100 e^t + 400 e^(4t)
The maximum will occur where P'(t) = 0
e^t = 4e^4t
1 = 4 e^3t
There will be one such point within 3 hours.